EXAMPLE 1 Evaluate numerical expressions a. (–4 2 5 ) 2 = Power of a product property Power of a power property Simplify and evaluate power. = 11 8 – 5 Negative exponent property Quotient of powers property Simplify and evaluate power. = 11 3 = 1331 = = 16,384 b –1 = (– 4) 2 (2 5 ) =

EXAMPLE 2 Use scientific notation in real life A swarm of locusts may contain as many as 85 million locusts per square kilometer and cover an area of 1200 square kilometers. About how many locusts are in such a swarm? Locusts SOLUTION Substitute values. = 85,000,

EXAMPLE 2 Use scientific notation in real life Write in scientific notation. = ( )( ) Use multiplication properties. Product of powers property Write 10.2 in scientific notation. Product of powers property = = = ( )( ) = The number of locusts is about , or about 102,000,000,000. ANSWER

GUIDED PRACTICE for Examples 1 and 2 Evaluate the expression. Tell which properties of exponents you used. 1. (4 2 ) ; Power of a power property 2. (–8)(–8) ; Product of a powers property ; Power of a quotient property ANSWER

GUIDED PRACTICE for Examples 1 and – ; quotient of power property ANSWER